Whenever people said, "You're so lucky!" he replied, "I'm so blessed." Among his blessings was his beloved wife Nancy A. Brady, who passed away in 1999.

Together, they founded the Washington, DC chapter of TRIO (Transplant Recipients International Organization). They were a source of information, comfort, and inspiration to many members of the transplant community.

In 2020, the Hypertrophic Cardiomyopathy Association recognized Claude as the first patient diagnosed with the heart condition, and dedicated September 18, as "Claude Brady" day.

In addition to his wife and parents, Claude was predeceased by his brother, George Brady, and step-son, Allen Whiddon. He leaves behind his granddaughter, Sarah Whiddon, sister-in-law, Nancy Brady, nephew, Matthew Brady (Dina), three grandnephews, and daughter-in-law, Cindy Burgett (Rod).

A memorial service is to be determined at a later date. He will be buried alongside his wife in Core, West Virginia.